Astrophysics

This is an application of Wein's Law that states the following:

, where is the wavelength of maximum emission of the object (measured in ), and is the temperature in . Since the wavelength and the temperature are inversely proportional, if we double the temperature, we must cut the wavelength by the same proportion. Therefore, the temperature must be halved.

Stefan-Boltzmann's equation for a blackbody states:

, where is the energy emitted each second, is the Stefan-Boltzmann constant, and is the temperature of the blackbody. Therefore, if we triple the temperature, the energy will increase by a factor of

The kinetic theory of gas states:

. Whenever the velocity of the individual gas particles is larger than the escape speed of the planet,

, the gas particles will leak into space and deplete the atmosphere. The physical property that determines this is the mass of the planet.